Steel and Composite Structures

  • 제31권1호
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  • Pages.43-51
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  • 2019
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Computation of mixed-mode stress intensity factors in functionally graded materials by natural element method

  • Cho, J.R. (Department of Naval Architecture and Ocean Engineering, Hongik University)
  • 투고 : 2018.07.11
  • 심사 : 2019.03.17
  • 발행 : 2019.04.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the numerical calculation of mixed-mode stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in non-homogeneous FGMs is reflected into the modified interaction integral ${\tilde{M}}^{(1,2)}$. The local NEM grid near the crack tip is refined, and the directly approximated strain and stress fields by PG-NEM are enhanced and smoothened by the patch recovery technique. Two numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The mixed-mode SIFs are parametrically computed with respect to the exponent index in the elastic modulus and external loading and the crack angle and compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately calculates the mixed-mode stress intensity factors of 2-D non-homogeneous functionally graded materials.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Anderson, T.L. (1991), Fracture Mechanics: Fundamentals and Applications, (1st Edition), CRC Press.
  4. Anlas, G., Santare, M.H. and Lambros, J. (2000), "Numerical calculation of stress intensity factors in functionally graded materials", Int. J. Fracture, 104, 131-143. https://doi.org/10.1023/A:1007652711735
  5. Apalak, M.K. (2014), "Functionally graded adhesively bonded joints", Rev. Adhesion Adhesive, 1, 56-84. https://doi.org/10.7569/RAA.2014.097301
  6. Atkinson, C. and List, R.D. (1978), "Steady state crack propagation into media with spatially varying elastic properties", Int. J. Eng. Sci., 16, 717-730. https://doi.org/10.1016/0020-7225(78)90006-X
  7. Ayhan, A.O. (2009), "Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements", Int. J. Solids Struct., 46(3-4), 796-810. https://doi.org/10.1016/j.ijsolstr.2008.09.026
  8. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., Int. J., 14(2), 103-115.
  9. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270.
  10. Belytschko, T., Lu, Y.Y., Gu, L. and Tabbara, M. (1995), "Element-free Galerkin methods for static and dynamic fracture", Int. J. Solids Struct., 32(17-18), 2547-2570. https://doi.org/10.1016/0020-7683(94)00282-2
  11. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164
  12. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  13. Bouderba, B. (2018), "Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environmental using an accurate theory", Steel Compos. Struct., Int. J., 27(3), 311-325.
  14. Bounouara, F., Benrahou, K., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  15. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., Int. J., 68(6), 661-675.
  16. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1) 19-30.
  17. Braun, J. and Sambridge, M. (1995), "A numerical method for solving partial differential equations on highly irregular evolving grids", Nature, 376, 655-660. https://doi.org/10.1038/376655a0
  18. Brighenti, R. (2005), "Application of the element-free Galerkin meshless method to 3-D fracture mechanics problems", Eng. Fract. Mech., 72, 2808-2820. https://doi.org/10.1016/j.engfracmech.2005.06.002
  19. Ching, H.K. and Batra, R.C. (2001), "Determination of crack tip fields in linear elastostatics by the meshless local Petrov-Galerkin (MLPG) method", Comput. Model. Eng. Sci., 2(2), 273-289.
  20. Cho, J.R. (2016), "Stress recovery techniques for natural element method in 2-D solid mechanics", J. Mech. Sci. Technol., 30(11), 5083-5091. https://doi.org/10.1007/s12206-016-1026-4
  21. Cho, J.R. and Ha, D.Y. (2002), "Optimal tailoring of 2D volumefraction distributions for heat-resisting functionally graded materials using FDM", Comput. Methods Appl. Mech. Engrg., 191, 3195-3211. https://doi.org/10.1016/S0045-7825(02)00256-6
  22. Cho, J.R. and Lee, H.W. (2006), "A Petrov-Galerkin natural element method securing the numerical integration accuracy", J. Mech. Sci. Technol., 20(1), 94-109. https://doi.org/10.1007/BF02916204
  23. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., 50, 609-614. https://doi.org/10.1115/1.3167098
  24. Dhaliwal, R.S. and Singh, B.M. (1978), "On the theory of elasticity of a nonhomogeneous medium", Int. J. Elasticity, 8, 211-219. https://doi.org/10.1007/BF00052484
  25. Dolbow, J.E. and Gosz, M. (2002), "On the computation of mixedmode stress intensity factors in functionally graded materials", Int. J. Solids Struct., 39(9), 2557-2574. https://doi.org/10.1016/S0020-7683(02)00114-2
  26. Eischen, J.W. (1987), "Fracture of nonhomogeneous materials", Int. J. Fracture, 34, 3-22. https://doi.org/10.1007/BF00042121
  27. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595.
  28. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded materials plates", Steel Compos. Struct., Int. J., 27(1), 109-122.
  29. Giannakopulos, A.E., Suresh, S. and Olsson, M. (1995), "Elastoplastic analysis of thermal cycling: layered materials with compositional gradients", Acta Metall. Mater., 43(4), 1335-1354. https://doi.org/10.1016/0956-7151(94)00360-T
  30. Gu, P., Dao, M. and Asaro, R.J. (1999), "A simplified method for calculating the crack tip field of functionally graded materials using the domain integral", J. Appl. Mech., 66(1), 101-108. https://doi.org/10.1115/1.2789135
  31. Irwin, G.R. (1957), "Analysis of stresses and strains near the end of a crack traveling a plate", J. Appl. Mech., 24, 361-364. https://doi.org/10.1115/1.4011547
  32. Jabbari, M., Sohrabpour, S. and Eslami, M.R. (2002), "Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads", Int. J. Pressure Vessel. Piping, 79(1), 493-497. https://doi.org/10.1016/S0308-0161(02)00043-1
  33. Kawasaki, K. and Watanabe, R. (2002), "Thermal fracture behavior of metal/ceramic functionally graded materials", Eng. Fract. Mech., 69(14-16), 1713-1728. https://doi.org/10.1016/S0013-7944(02)00054-1
  34. Khayat, M., Poorveis, D. and Moradi, S. (2017), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Steel Compos. Struct., Int. J., 23(1), 1-16. https://doi.org/10.12989/scs.2017.23.1.001
  35. Kim, J.H. and Paulino, G.H. (2002), "Finite element evaluation of mixed mode stress intensity factors in functionally graded materials", Int. J. Numer. Methods Eng., 53, 1903-1935. https://doi.org/10.1002/nme.364
  36. Konda, N. and Erdogan, F. (1994), "The mixed mode crack problem in a non-homogeneous elastic medium", Eng. Fract. Mech., 47(4), 533-545. https://doi.org/10.1016/0013-7944(94)90253-4
  37. Liu, K.Y., Long, S.Y. and Li, G.Y. (2008), "A meshless local Petrov-Galerkin method for the analysis of cracks in the isotropic functionally graded material", Comput. Model. Eng. Sci., 7(1), 43-57.
  38. Mahbadi, H. (2017), "Stress intensity factor of radial cracks in isotropic functionally graded solid cylinders", Eng. Fract. Mech., 180, 115-131. https://doi.org/10.1016/j.engfracmech.2017.05.019
  39. Menasria, A, Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175.
  40. Meziane, M.A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  41. Miyamoto, Y., Kaysser, W.A., Rabin, B.H. and Kawasaki, A. (2013), Functionally Graded Materials: Design. Processing and Applications, Springer Science & Business Media.
  42. Noda, N. (1999), "Thermal stresses in functionally graded materials", J. Thermal Stress., 22(4-5), 477-512. https://doi.org/10.1080/014957399280841
  43. Rao, B.N. and Rahman, S. (2000), "An efficient meshless method for fracture analysis of cracks", Comput. Mech., 26, 398-408. https://doi.org/10.1007/s004660000189
  44. Rao, B.N. and Rahman, S. (2003), "Mesh-free analysis of cracks in isotropic functionally graded materials", Eng. Fract. Mech., 70, 1-27. https://doi.org/10.1016/S0013-7944(02)00038-3
  45. Reiter, T. and Dvorak, G.J. (1998), "Micromechanical models for graded composite materials: II. Thermomechanical loading", J. Phys. Solids, 46(9), 1655-1673. https://doi.org/10.1016/S0022-5096(97)00039-2
  46. Rizov, V.I. (2017), "Fracture analysis of functionally graded beams with considering material nonlinearity", Struct. Eng. Mech., Int. J., 64(4), 487-494.
  47. Sidhoum, I.A., Boutchicha, D., Benyoucef, S. and Tounsi, A. (2017), "An original HSDT for free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 25(6), 735-745.
  48. Sukumar, N., Moran, A. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Methods Eng., 43, 839-887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R
  49. Tilbrook, M.T., Moon, R.J. and Hoffman, M. (2005), "Crack propagation in graded composites", Compos. Sci. Technol., 65(2), 201-220. https://doi.org/10.1016/j.compscitech.2004.07.004
  50. Vel, S.S. and Goupee, A.J. (2010), "Multiscale thermoelastic analysis of random heterogeneous materials, Part I: microstructure characterization and homogenization of material properties", Comput. Mater. Sci., 48, 22-38. https://doi.org/10.1016/j.commatsci.2009.11.015
  51. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., Int. J., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161
  52. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  53. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., Int. J., 14(6), 519-532.
  54. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  55. Zhang, Ch., Sladek, J. and Sladek, V. (2004), "Crack analysis in unidirectionally and bidirectionally functionally graded materials", Int. J. Fract., 129, 385-406. https://doi.org/10.1023/B:FRAC.0000049495.13523.94

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